Chapter 10 Polynomial and Series Representations of Functions

Index
About this Chapter

Section 10.1 Sums and Limits
10.1.1 Geometric Sums
10.1.2 More Notation for Limits
Section Summary
Exercises

Section 10.2 Approximation of Functions: Taylor Polynomials
10.2.1 Coefficients of Polynomials
10.2.2 Taylor Polynomials for ex
10.2.3 Taylor polynomials for sin x
Section Summary
Exercises

Section 10.3 Taylor Series
10.3.1 What Happens as the Degree Increases?
10.3.2 Sequences and Series
10.3.3 Taylor Series for ex and sin x
10.3.4 The Error Function
Section Summary
Exercises

Section 10.4 More Taylor Polynomials and Series
10.4.1 Geometric Sums Revisited
10.4.2 Taylor Polynomials and Series for ln(1+x)
10.4.3 Taylor Polynomials and Series for arctan(x)
Section Summary
Exercises

Section 10.5 Series of Constants
10.5.1 Convergence and Divergence
10.5.2 The Harmonic Series
10.5.3 The Alternating Harmonic Series
10.5.4 The Leibniz Series
Section Summary
Exercises

Section 10.6 Convergence of Series
10.6.1 The Alternating Series Test
10.6.2 Convergence of the Arctangent Series
10.6.3 Convergence of the Logarithmic Series
10.6.4 Using Geometric Series to Estimate Tails:
           Exponential Series
10.6.5 Using Geometric Series to Estimate Tails:
           Logarithmic Series
10.6.6 Convergence of the Taylor Series for Sine and Cosine
10.6.7 The Ratio Test
Section Summary
Exercises

Chapter Summary
Chapter Review
Concepts and Applications
Formulas